System and method to estimate compressional to shear velocity (VP/VS) ratio in a region remote from a borehole

ABSTRACT

In some aspects of the disclosure, a method for creating three-dimensional images of non-linear properties and the compressional to shear velocity ratio in a region remote from a borehole using a conveyed logging tool is disclosed. In some aspects, the method includes arranging a first source in the borehole and generating a steered beam of elastic energy at a first frequency; arranging a second source in the borehole and generating a steerable beam of elastic energy at a second frequency, such that the steerable beam at the first frequency and the steerable beam at the second frequency intercept at a location away from the borehole; receiving at the borehole by a sensor a third elastic wave, created by a three wave mixing process, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole; determining a location of a three wave mixing region based on the arrangement of the first and second sources and on properties of the third wave signal; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and determining at a plurality of azimuths, inclinations and longitudinal locations within the borehole. The method is additionally used to generate three dimensional images of the ratio of compressional to shear acoustic velocity of the same volume surrounding the borehole.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit from U.S. Provisional Application No.61/170,070 filed on Apr. 16, 2009, incorporated herein by reference inits entirety, under 35 U.S.C. §119(e).

GOVERNMENT RIGHTS

This invention was made with Government support under CooperativeResearch and Development Agreement (CRADA) Contract NumberDE-AC52-06NA25396 awarded by the United States Department of Energy. TheGovernment may have certain rights in this invention.

FIELD

The present invention relates generally to seismic interrogation of rockformations and more particularly to creating three-dimensional images ofnon-linear properties and the compressional to shear velocity ratio in aregion remote from a borehole using a combination of sources in aborehole configured to provide elastic energy, and receiving andanalyzing a resultant third wave formed by a three wave mixing process.

BACKGROUND

Acoustic interrogation of subsurface features tends to be limited by thesize and power of practical sources, and in practice, the output of downhole acoustic transducers is limited by the power transmissioncapabilities of the wireline cable. High frequency signals have arelatively short penetration distance, while low frequency signalsgenerally require large sources, clamped to the borehole wall, tomaximize energy transfer to the formation and minimize unwanted signalswithin the well bore. Currently, acoustic borehole tools are designedwith acoustic sources in the borehole to detect returning acoustic wavesthat are propagating along the borehole walls or scattered byinhomogeneities of linear properties of rock formations surrounding theborehole. U.S. Pat. No. 7,301,852 by Leggett, III et al. discloses aLogging While Drilling tool, designed to detect rock formationboundaries, with two acoustic source arrays emitting from a boreholegenerating a third wave by assumed non-linear mixing in rocks at thelocation of intersection of the acoustic signals. The third wave isscattered by heterogeneities in subsurface properties, and the scatteredsignal is detected by sensors in the logging tool. The source arrays aremerely disclosed to be directional without any further description.

Attempts have been made to characterize the non-linear properties of aformation in the area of oil and gas prospecting from boreholes, buteach has its own limitations. For example, U.S. Pat. No. 5,521,882 byD'Angelo et al. discloses an acoustic tool designed to record withpressure receivers the non-linear waves that propagate along theborehole wall with limited penetration into the surrounding rockformation and refract back into the well bore fluid. U.S. Pat. No.6,175,536 by Khan discloses a method to estimate the degree ofnon-linearity of earth formations from spectral analysis of seismicsignals transmitted into the formation from one borehole and received ina second borehole. In light of these prior attempts, there is a need foran apparatus and method for generating three-dimensional images ofnon-linear properties in a remote region from a borehole.

SUMMARY

In accordance with some aspects of the disclosure, a method for creatingthree-dimensional images of non-linear properties in a region remotefrom a borehole using a conveyed logging tool is disclosed. The methodincludes arranging with a specific spatial configuration a first sourcein the borehole and generating a steerable primary beam of elasticenergy at a first frequency; arranging a second source in the boreholeand generating a steerable primary beam of elastic energy at a secondfrequency, such that the two steerable beams intercept at a locationaway from the borehole; receiving by an array of sensors at the boreholethe arrival of the third elastic wave, created by a three wave mixingprocess in the rock formation, with a frequency equal to a differencebetween the first and second primary frequencies, that propagates backto the borehole in a specific direction; locating the three wave mixingregion based on the arrangement of the first and second sources and onthe properties of the third wave signal; and creating three-dimensionalimages of the non-linear properties using data recorded by repeating thegenerating, receiving and locating steps at a plurality of azimuths,inclinations and longitudinal locations within the borehole.

In accordance with some aspects of the disclosure, a method for creatingthree-dimensional images of non-linear properties in a region remotefrom a borehole using a conveyed logging tool is disclosed. The methodincludes arranging with a specific spatial configuration a first sourcein the borehole and generating a primary wave of elastic energy at afirst frequency; arranging a second source in the borehole andgenerating a primary wave of elastic energy at a second frequency;receiving by an array of three component sensors at the borehole thearrival of the third elastic wave created by a three wave mixingprocess, with a frequency equal to a difference between the first andsecond primary frequencies, that propagates back to the borehole;determining the propagation direction of the third wave from the signalsreceived by the sensor array; imaging the locus of the three wave mixingregion based on the arrangement of the first and second sources and thepropagation direction of the third wave; and creating three-dimensionalimages of the non-linear properties using data recorded by repeating thegenerating, receiving, determining and imaging steps at a plurality ofazimuths, inclinations and longitudinal locations within the borehole.

In accordance with some aspects of the disclosure, further methods forcreating three-dimensional images of non-linear properties in a regionremote from a borehole using a conveyed logging tool are disclosed.These share the common configuration of two sources and an array ofsensors in the borehole, but differ in that the one or other of thesources may generate a steerable beam or a wave of elastic energy, andthe sensor units in the array may be a combination of non-directionaland three component devices. The method includes arranging with aspecific spatial configuration a first source in the borehole andgenerating either a steerable primary beam of elastic energy or aprimary wave of elastic energy at a first frequency; arranging a secondsource in the borehole and generating either a steerable primary beam ofelastic energy or a primary wave of elastic energy at a secondfrequency, such that the energy from the two sources mixes at locationsaway from the borehole; receiving by a sensor array at the borehole thedirect arrival of the third elastic wave, created by a three wave mixingprocess, with a frequency equal to a difference between the first andsecond primary frequencies, that propagates back to the borehole in aspecific direction; locating the three wave mixing region based on thearrangement of the first and second sources and on properties of thethird wave signal; and creating three-dimensional images of thenon-linear properties using data recorded by repeating the generating,receiving and locating steps at a plurality of azimuths, inclinationsand longitudinal locations within the borehole.

In accordance with some aspects of the disclosure, three dimensionalimages of the non-linear properties of the formations surrounding theborehole are transformed to reservoir properties using appropriaterelations between formation non-linearity and said properties. Theimages may be of properties at the time of logging, or may representchanges between two logging runs separated by the passage of time.

In accordance with some aspects of the disclosure, methods to createthree dimensional images of the ratio of compressional to shear acousticvelocity of rocks surrounding the borehole are disclosed. These methodsare variations of the methods for creating three dimensional images ofnon-linear properties discussed above.

In accordance, with some aspects of the disclosure, an apparatus forcreating three-dimensional images of non-linear properties and thecompressional to shear velocity ratio of the rock formations remote froma borehole using a conveyed logging tool is disclosed. The apparatusincludes a first source arranged in the borehole and configured togenerate a steerable beam or a wave of elastic energy at a firstfrequency; a second source arranged in the borehole and configured togenerate a steerable beam or a wave of elastic energy at a secondfrequency, such that the beams or waves at the first frequency and thesecond frequency intercept at a location away from the borehole; and anon-directional or three component sensor array configured to receive athird elastic wave if that the non-linear properties of the region ofinterest result in the creation of the third elastic wave by a threewave mixing process having a frequency equal to a difference of thefirst and the second frequencies and a specific direction of propagationback to the borehole; a first processor arranged in the borehole tocontrol source firing and recording of the third elastic wave; a deviceconfigured to transmit data up-hole through a wireline cable for awireline tool; and a second processor arranged to create thethree-dimensional images based, in part, on properties of the receivedthird wave and the arrangement of the first and second sources.

These and other objects, features, and characteristics of the presentinvention, as well as the methods of operation and functions of therelated elements of structure and the combination of parts and economiesof manufacture, will become more apparent upon consideration of thefollowing description and the appended claims with reference to theaccompanying drawings, all of which form a part of this specification,wherein like reference numerals designate corresponding parts in thevarious Figures. It is to be expressly understood, however, that thedrawings are for the purpose of illustration and description only andare not intended as a definition of the limits of the invention. As usedin the specification and in the claims, the singular form of “a”, “an”,and “the” include plural referents unless the context clearly dictatesotherwise.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a configuration for creating three-dimensional images ofnon-linear properties in a region remote from a borehole in accordancewith various aspects of the disclosure

FIG. 2 shows a configuration for creating three-dimensional images ofnon-linear properties in a region remote from a borehole in accordancewith aspects of the disclosure.

FIG. 3 shows a configuration for creating three-dimensional images ofnon-linear properties in a region remote from a borehole in accordancewith aspects of the disclosure.

FIG. 4 shows a flow chart for creating three-dimensional images ofnon-linear properties in a region remote from a borehole in accordancewith various aspects of the disclosure.

FIGS. 5 a, 5 b and 5 c shows a numerical simulation of selection rule 1for a beam-beam interaction of Table 1 when the two primary waves arebeams.

FIG. 6 illustrates the geometry of the generation of the differencefrequency third wave by non-linear mixing of two primary acoustic wavesas governed by the non-linear mixing selection rule.

FIG. 7 shows an application of aspects of the disclosure for imagingusing a beam and broad beam or plane wave.

DETAILED DESCRIPTION

FIG. 1 shows one of several possible configurations for creatingthree-dimensional images of non-linear properties and the compressionalto shear velocity ratio in a region remote from a borehole in accordancewith various aspects of the disclosure. First source 105 is arranged inborehole 110 to generate a steerable primary beam of acoustic energy ata first frequency f₁. Second source 115 is also arranged in borehole 110to generate a steerable primary beam of acoustic energy at a secondfrequency f₂. By way of a non-limiting example, both first source 105and second source 115 may be a phased array of sources and may beconfigured to generate either compressional or shear steerable beams.

As shown in FIG. 1, first source 105 is arranged on first tool body 120and second source 115 is arranged on second tool body 125. However, thedisclosure is not so limiting as first tool body 120 and second toolbody 125 may also be arranged together on a common tool body (notshown). Tool bodies 120 and 125 are arranged to be independentlymoveable within bore hole 110 in at least two degrees of freedomincluding translation along the longitudinal axis 150 of borehole 110and rotation 155 in azimuth about the longitudinal axis of borehole 110.First source 105 may be arranged above or below second source 115 inborehole 110. Tool bodies 120 and 125 may be arranged on a conveyedlogging tool (not shown) within borehole 110.

For a given azimuth orientation of first source 105 and second source115, the beam generated by second source 115 and the beam generated byfirst source 105 are configured such that the beams converge andintercept in a mixing zones 130 remote from borehole 110. By acombination of independently steering the beams and changing theseparation between the sources 105, 115, the mixing zones 130 move inthe plane defined by the beams and the longitudinal borehole axis 150,while controlling the angle of interception. The distance of mixingzones 130 from borehole 110 can range from near the edge of borehole 110to about 300 meters into the surrounding subsurface rock formation. Byway of a non-limiting example, the phase difference and/or time delaysbetween adjacent elements in the source array may be modified to focusthe acoustic energy of the primary beams at a particular mixing zone.

The non-linear properties of the earth at the location between the twowaves result in the generation of a third elastic wave. The thirdelastic wave is a result of a three-wave mixing process that occurs innonlinear materials, in this case, rock formations. In this process, twoconverging non-collinear waves of different frequencies, f₁ and f₂, alsocalled primary waves, mix to form additional waves at the harmonic andintermodulation frequencies f₁−f₂, f₁+f₂, 2×f₁; and 2×f₂, etc. Thestrength of the third wave is a function the non-linearity of the rocksin the mixing zones. By way of a non-limiting example, when a primarycompressional (P) wave with a frequency f₁ and a primary shear (SV) wavewith a frequency f₂ cross in a non-linear medium, a third compressional(P) or shear (SV) wave is generated with a frequency f₁−f₂. For furtherdescription, see Johnson et al. (1987) and Johnson and Shankland (1989),which is hereby incorporated by reference in its entirety.

As further discussed below under propagation selection rules, the thirdwave propagation vector is co-planar with the propagation vectors of thetwo primary waves. Certain combinations of angle of intersection, f₁/f₂ratio and compressional to shear velocity ratio result in a thirdelastic wave with frequency f₁−f₂ propagating in a specific anglerelative to the primary beams back to the borehole 110.

Sensor or receiver array 135 is arranged at specific location inborehole 110 to detect the third wave returning to the borehole 110. Insome aspects of the disclosure, as shown in the Figure, sensor array 135comprises more than one sensor arranged as an array of sensors on sensortool body 140 and separate from tool bodies 120 and 125. Sensor 135 isconfigured to be independently moveable within bore hole 110 along thelongitudinal axis 150 of borehole 110. In some aspects, sensor tool body140 is arranged below tool bodies 120 and 125 or arranged above andbelow tool bodies 120 and 125. In some aspects, sensor tool body 140 isconnected to either or both tool bodies 120 and 125.

The third wave is detected at borehole 110 by sensor array 135. FIG. 2shows an arrangement similar to FIG. 1, wherein receiver 135 is replacedby three component geophone 145 clamped to the borehole walls. Theresultant signal is decomposed by processing into its inclination andazimuth in order to add redundancy to the system by determining thedirection of the incoming third wave arrival.

In some aspects, a first processor configured to executemachine-readable instructions (not shown) may be arranged in borehole110 to perform various processing tasks, such as controlling sourcefiring and compressing or filtering the data recorded by sensor array135. A second processor configured to execute machine-readableinstructions (not shown) may be arranged outside borehole 110 to assistthe first processor or perform different processing tasks than the firstprocessor. For example, the second processor may perform part or allprocessing activities in creating the three-dimensional images. Atransmitter or transceiver (not shown) may be arranged in borehole 110to transmit data up-hole through a wireline cable (not shown).

At a given depth along the borehole of one of the sources 105, 115,sweeping the beams in inclination at constant relative bearing tospatially scan the mixing zone in a plane passing through the boreholeaxis, rotating the sources azimuthally to rotationally scan the mixingregion and moving the whole assembly along borehole 110, results inscanning a 3D volume of mixing zones around the borehole for non-linearproperties. With sources 105, 115 and sensor array 135 located onindependent tool bodies, high redundancy in the data can be obtained andthe depth of investigation can be varied. In this way, a 3D volume ofthe rocks surrounding the borehole can be interrogated for non-linearproperties and a 3D image of non-linear properties can be processed andcomputed from the returned signals.

FIG. 3 shows another arrangement for creating three-dimensional imagesof non-linear properties in a region remote from a borehole inaccordance with various aspects of the disclosure. The arrangement ofFIG. 3 is similar to the arrangement in FIG. 2, with the primarydifference being that the sources are arranged in borehole 110 toproduce elastic waves instead of steerable beams. With reference to FIG.3, first source 305 is arranged in borehole 110 on first tool body 320to generate a first elastic wave of acoustic energy at a first frequencyf₁. Second source 315 is arranged in borehole 110 on second tool body325 to generate a second elastic wave of acoustic energy at a secondfrequency f₂. First and second elastic waves produced by sources 305,315 are arranged to intercept away from borehole 110 at various mixingzones 130. Receiver 145 is arranged within borehole 110 to receive athird wave that is produced in the mixing zones 130 by the three-wavemixing process discussed above, and further discussed below. Since thewaves produced by sources 305, 315 are essentially non-directional,mixing between the waves occurs simultaneously in the entire area ofmixing zones 130, that also extends out of the plane of the Figure, andreceiver 145 tends to have directional characteristics. By way of anon-limiting example, a three component geophone array may be used forthis purpose. The resultant signal is decomposed by processing intomultiple arrival signals at a range of inclinations and azimuths andtravel times. Given the locations of sources and the receivers, thetravel times and directions of each decomposed directional arrival,there is sufficient information to apply the selection rules describedbelow to determine a unique mixing zone where the third wave wasgenerated. This unique mapping allows the construction of a threedimensional image from the properties of the received signal.

FIG. 4 shows a method for creating three-dimensional images ofnon-linear properties and the compressional to shear velocity ratio in aregion remote from a borehole using a conveyed logging tool. The methodbegins at 405 where a first source is arranged in the borehole togenerate a steerable beam elastic energy at a first frequency and asecond source is arranged in the borehole to generate a steerable beamof elastic energy at a second frequency. The steerable beams at thefirst and second frequency are arranged to intercept at a location awayfrom the borehole. As such, the second beam is generated at the sameazimuth as the first beam, but at a different inclination relative tothe longitudinal axis of the borehole. The method continues at 410 wherea third elastic wave is received at the borehole by a sensor array. Asdiscussed above, the third elastic wave is created by a three wavemixing process, with a frequency equal to a difference between the firstand second frequencies and a direction of propagation towards theborehole. At 415, a three wave mixing location away from the borehole isdetermined from the arrangement of the first and second sources andproperties of the third wave, by recourse to the selection rulesdiscussed below. At 420, three-dimensional images are created of thenon-linear properties using data recorded by repeating the generating ofstep 405, the receiving of step 410 and the determining of step 415 at aplurality of azimuths, inclinations and longitudinal locations withinthe borehole. In cases of compressional-shear interaction the receivedsignals are analyzed in step 425 for the compressional/shear velocity(Vp/Vs) ratio. At 430, the non-linear properties are transformed tophysical reservoir properties such as fluid saturation, effectivestress, fracture density and mineralogy.

In some aspects of the present disclosure, the first and second sourcesmay be beam or cylindrical or spherical wave sources, and the sensorarray may be any combination of non-directional single component sensorsand three component geophones. Alternative permutations of the componentparts offer different degrees of redundancy in signal processing andimaging.

Experimental demonstrations of non-linear mixing of two acoustic wavesin solid have been reported, for example by Rollins, Taylor and Todd(1964), Johnson et al. (1987) and Johnson and Shankland (1989), whichare hereby incorporated by reference in their entirety. In the specialcase where a primary compressional (P) wave with a frequency f₁ and aprimary shear (S) wave with a frequency f₂ cross each other, in anon-linear medium, a third P or S wave is generated with the frequencyf₁−f₂. If the primary P and S waves are beams with wave vectors k₁ andk₂, respectively, and the non-linear formation property is uniform, thekinematics of wave interaction requires the resulting third wave to be aplane wave with wave vector k₃ that obeys the selection rule k₁−k₂=k₃.The selection rule imposes a very tight restriction on the permissiblecrossing angles for the primary waves and a specific propagationdirection of the third wave. The general kinematic theory for non-linearmixing of two linear plane waves and the selection rules and amplituderesponses have contributions from Jones and Kobett (1963), Rollins,Taylor et al. (1964) and later by Korneev, Nihei and Myer (1998), all ofwhich are hereby incorporated by reference in their entirety, who alsoprovide specific relationships between non-linear parameters of themixing medium and the non-linear mixing signal strength. For example,Equation 53 and 54 of Korneev, Nihei and Myer show that the mixingstrength of P and SV (vertically polarized shear) plane waves isproportional to a specific combination of non-linear parameters of therocks.

The selection rules of Korneev, Nihei and Myer governing the nonlinearinteraction of two elastic plane waves can be used as guidance for theinteraction of two elastic beams. These plane wave selection rulesdictate that the following six nonlinear interactions producebackscattered waves.

Table 1—Selection Rules Governing Non-Linear Interaction of Two ElasticPlane Waves. In this table, and elsewhere in this document, f₁ isgreater than f₂.

Selection 1^(st) beam 2^(nd) beam Resultant 3^(rd) beam or Rules or waveor wave wave from 1^(st) + 2^(nd) 1 P(f₁) SV(f₂) P(f₁ − f₂) 2 P(f₁)SV(f₂) SV(f₁ − f₂) 3 P(f₁) SH(f₂) SH(f₁ − f₂) 4 P(f₁) SV(f₂) P(f₁ + f₂)5 SV(f₁) SV(f₂) P(f₁ + f₂) 6 SH(f₁) SH(f₂) P(f₁ + f₂)

FIGS. 5 a, 5 b and 5 c shows a numerical simulation of selection rule 1of Table 1 when the two primary waves are beams of a beam-beaminteraction. A 25 kHz compressional beam, shown in FIG. 5 a, and a 18kHz shear beam, shown in FIG. 5 b, mix to form a third beam, shown inFIG. 5 c, with frequency 7 kHz=25 kHz−18 kHz. In this example, inaccordance with the plane wave predictions of Korneev, Nihei and Myer, athird back propagating P beam with frequency (f₁−f₂) at an angle of 133°to the P(f₁) wave is generated by nonlinear mixing in the region wherethe P(f₁) and SV(f₂) beams overlap.

The kinematics of non-linear interactions of beams results in thegeneration of specific combinations of wave vectors and frequencies. Thethird wave returns at a specific travel time, and with specificfrequencies f₃ and wave vectors k₃ such as f₃=f₁−f₂ and k₃=k₁−k₂. For acombination of f₁, f₂, k₂ and k₃, there is a well-defined propagationwave vector k₃ of the third wave in the same plane, defined by k₁ andk₂. There is a direct correspondence between the signal detected at aparticular receiver position and the location where the non-linearmixing of the two primary waves k₁ and k₂ takes place. The signalstrength of the receiver would be proportional to the strength of thenon-linearity of the rocks in the mixing zone, among other factors, andreach a maximum for a receiver lying on vector k₃. Therefore, the signalstrength at the receivers can be geometrically mapped onto thenon-linearity of the rocks along the beam trajectory as indicated byFIG. 1.

The geometrical theory of wave propagation indicates that the beamgenerated in each interaction zone would arrive at the borehole at aspecific receiver defined by the geometry of the three wave vectors k₁,k₂ and k₃, after a specific time delay. The strength of the returningsignal at a specific location in the borehole at a particular time isdependent on the degree of non-linearity of the interaction location,and hence a time image of the relative strength of the non-linearproperties of the rocks along the beam can be constructed. The amplitudemagnitude of a returned signal at the receivers is itself indicative ofcertain petrophysical properties of the mixing zone. If the beam andplane wave are scanned in azimuth and inclination while preserving thenecessary convergence angle, a localized circumferential and radial 3Dimage of non-linear properties of rocks surrounding the borehole can beobtained. By moving the entire assembly up and down the borehole,repeated 3D images of non-linear properties of rocks surrounding theborehole are obtained. By making weighted stacks of these repeatedimages, a final image of non-linear properties of rocks surrounding theentire borehole can be constructed through subsequent computerprocessing. In addition, if the sources and the receivers are part ofthree separate tool bodies, one or two can be moved while the third oneis fixed (for example, the sources are fixed while the receiver toolbody is moved up and down). Alternatively, several descents into thewell may be made with different spacing between the tool bodies.

For non-linear mixing between an elastic beam and a broader beam (quasiplane wave), the selection rule is relaxed. Third waves of frequencyf₁−f₂, centered around the wave vector k₃=k₁−k₂, are generatedcontinuously along the primary beam if the beam width is about tenwavelengths of the third wave. The resulting signal strength forf₃=f₁−f₂ is a function of the average non-linear properties of themixing region, the average ratio of velocity offi propagation andaverage velocity for f₂ propagation (noting that f₁ and f₂ may becompressional or shear), the volume of the mixing zone and the geometryof the mixing. This function can be computed for various mixing modes.For example, the signal strength for a particular important mixing modesuch as compressional wave P for f₁ and SV for f₂ is given by

$\begin{matrix}{U = {2\pi^{2}\beta_{{PS}_{v}P}A_{1}B_{2}\frac{f_{1}{f_{2}\left( {f_{1} - f_{2}} \right)}}{V_{P}^{2}V_{s}}\frac{V_{{PS}_{v}P}}{r}F_{{PS}_{v}P}\Delta_{{PS}_{v}P}}} & (1)\end{matrix}$where U is the displacement amplitude of the third wave received at theborehole, A₁ is the longitudinal polarization of the compressional waveand B₂ is the transverse polarization of the shear wave. β is a functionof the A, B and C parameters of Landau and Lifschitz representing thenon-linearity of the rocks in the mixing zone. v is the volume of themixing zone, r is the distance from mixing zone to the receiver. F isthe geometric form factor of order 1 which is dependent on the geometryof the incident beams and can be numerically computed from the Korneev,Nihei, Myers theory for the particular geometry. A is a selection ruleform factor which is a numerically computable function of the wavevectors k₁, k₂ and k₃ and is only significant if the interactiongeometry honors the selection rules. The subscript PS_(v)P in theformula refers to compressional-shear interaction generating acompressional wave.

In accordance with certain aspects of this disclosure, an image of thecompressional to shear velocity ratio may be constructed as follows.When one of the sources generates a compressional wave (P-wave) withfrequency f₁ and the other source generates an SV-wave with frequency f₂and both waves are steered towards a specific mixing volume, thepropagation direction of the third compressional wave (P-wave) withdifference frequency f₃=f₁−f₂ is controlled by the average in situ Vp/Vsratio of the rock in the mixing zone as governed by the selection rulesas shown in FIG. 6. From the measurements of the signal in the threecomponent receiver array 145 on FIG. 2 or FIG. 3, the direction of thisthird wave can be determined and thereby, the in situ Vp/Vs of themixing zone can be computed. If the beam and plane wave are scanned inazimuth and inclination while preserving the necessary convergenceangle, a localized circumferential and radial 3D image of in situ Vp/Vsratio of rocks surrounding the borehole can be obtained. By moving theentire assembly up and down the borehole, repeated 3D images of in situVp/Vs of rocks surrounding the borehole may be obtained. By makingweighted stack of these repeated images, a final image of in situ Vp/Vsof rocks surrounding the entire borehole can be constructed throughsubsequent computer processing. Alternatively, several descents into thewell may be made with different fixed spacing between the tool bodies.

In some aspects of this disclosure, an alternative determination ofVp/Vs ratio is achieved through scanning the ratio of the frequencies f₁to f₂ of the primary beams. FIG. 6 illustrates the geometry of theinteraction of two beams such as those generated in the configuration ofFIG. 1, that may be analyzed using the vector mathematics andtrigonometry described above. The lengths k₁ and k₂ of vectors k₁ and k₂are defined by the ratio of their corresponding frequencies andvelocities. As shown in FIG. 6, the returning angle γ is a function off₁/f₂, Vp/Vs ratio and the intersection angle θ of the two primarybeams. In addition, the physical selection rules only permit thegeneration of a third wave at specific combinations of f₁/f₂, Vp/Vsratio and angle of interception 0, such as the example illustrated onFIG. 5.

Using the symbol r for the Vp/Vs ratio and the terms defined on FIG. 6,the magnitude k₃ of vector k₃ is given by the vector sum of k₁ and −k₂,that is k₃=|k₁−k₂|=

$k_{3} = {{{k_{1} - k_{2}}} = \frac{f_{1} - f_{2}}{V_{p}}}$and also by the cosine rule that states k₃ ²=k₁ ²−k₂ ²−2k₁k₂ cos θ.Combining the two equations, and substituting f₁/Vp for k₁ and f₂/Vs fork₂, leads to a statement of the geometric conditions imposed by theselection rules. The quadratic equation

${{\frac{f_{2}}{f_{1}}r^{2}} - {2\mspace{14mu}\cos\;\theta\; r} - \frac{f_{2}}{f_{1}} + 2} = 0$may be solved for r, the VpVs ratio of the mixing zone. This leads to anon-limiting alternative method for measuring in situ Vp/Vs ratio of aparticular mixing region by the following sequence: a) record a standardsonic waveform log to determine Vp and Vs near the wellbore to acquiredata to estimate the phase differences between adjacent elements in aphased source array to steer the beams at the approximate convergenceangle for the geometry of the planned measurement; b) steer the P and SVsources to converge at a controlled angle θ and mix at a particularregion in space surrounding the borehole; c) vary f₂ while fixing f_(i)and measure the amplitude of the received signal at the differencefrequency f₁-f₂ at the sensors in the borehole; d) identify thefrequency at which the signal each receiver in the array reaches amaximum amplitude strength; and e) determine angles θ and φ from thegeometry of the sources and receivers. By sweeping the beams ininclination, rotating in azimuth, and moving the entire assembly up anddown the borehole and repeating the above procedure, the VpVs ratio of a3D volume around the borehole is interrogated and thereby 3D images ofin situ Vp/Vs ratio of rocks surrounding the borehole may be obtained.

The methods described above offer an advantageous property in that thefrequency difference f₁−f₂ is very specific, allowing for spectralanalysis to enhance the signal to noise ratio of the measurements.Moreover, if both frequencies f₁ and f₂ are simultaneously chirpedproportionally, the resulting difference frequency signal f₁−f₂ wouldalso be a well defined chirped signal. The time-varying code may includeone or more of a variation in amplitude, a variation in frequency,and/or a variation in phase of the first, the second, or both the firstand the second beams or waves. The third difference wave can be broadband if one of the primary frequencies is swept through a range offrequencies while their frequency ratio is fixed. Thus, the resultingthird beam f₂−f₁ will be swept across a wide frequency range, whilepreserving the same direction. This allows for improvement in signal tonoise by standard auto-correlation of the chirped or coded signal.

Since the wave vector k₃=k₁−k₂ is well defined, the signal to noisediscrimination of the recorded third wave from receivers 135 can beenhanced further by employing three-component receivers in the borehole.The signals from the three components can be tuned to specificdirectivity by a technique, such as, hodogram analysis.

In some aspects of the present disclosure, the signal to noise ratio canbe improved by repeating the above steps with an inverse polarity (180degrees out of phase) and adding the results together. The returningdifference frequency signal will add coherently as its amplitude isproportional to the product of the amplitudes of the two primary wavesand therefore will not reverse polarity when the polarity of the primarysource is reversed, while any linear noises generated by the primarywaves in the system will reverse polarity and cancel upon addition.

Alternative methods can be devised with various non-exclusivecombinations of beams and waves. By way of a non-limiting example, amethod to generate images by computer processing of acoustic and seismicsignals includes the follow steps. First, perform spectral analysis ofthe frequency content of the recorded third wave and applicableselection rules of the difference frequency signal in order to isolatethe third wave signal generated by the non-linear mixing process. In thecase that the sensors include three component geophones, determine thedirection of the third wave impinging on the borehole using orientationtechniques. The method continues by analyzing the amplitude of therecorded third wave as a function of frequency ratios of the primarymixing waves and determining the mixing location where the third wavesignals originated, from the selection rules of non-collinear mixing innon-linear media, the wavenumbers of the first and second beams and thethird wave and the locations of the two beam sources and the sensorarray. The method continues by constructing seismograms determined bycross-correlation of the received signals with chirped transmittersignals for each source-receiver combination. The method continues byperforming three dimensional time or depth imaging to the entire dataset, in order to obtain three dimensional images of the non-linearproperties of the formation surrounding a borehole in either or both oftime and distance. The methods for generating images from seismogramsare known, for example, Hill et al., which is hereby incorporated byreference, have provided the general methodology for the special case ofimaging from beams.

Another non-limiting alternative imaging method is illustrated on FIG.7, which shows the case of interactions of a narrow 705 and a broad(wide) beam 710. Given a smooth background model of Vp and Vs of theinvestigated volume, application of the selection rules enables thegeometric mapping of the energy detected at a receiver location 735 onto mixing zones 730 along the narrow beam. A time image of thenon-linear property can thus be constructed along the narrow beam. Byrotating in azimuth and moving the assembly along the borehole, a threedimensional time image can be constructed of a volume centered on theborehole. Successive repetition of the measurement at different beaminclinations, and altering the f₂/f₁ frequency ratio α yields a seriesof three dimensional time images. This redundancy in imaging permits thefurther refinement of the smooth background model and a threedimensional spatial image.

Non-linear parameters of rocks have been found to be related to a numberof important hydrocarbon reservoir parameters, such as variations withgas, oil and water saturation, effective stress, fracture density andmineralogical content. For example, see Ostrovsky and Johnson 2001,which is hereby incorporated by reference. In certain aspects of thisdisclosure, the 3D images of non-linear properties constructed by thismethod are transformed to provide quantitative information on thedistribution of these properties around the borehole at the time ofrecording. In addition, sequential repetitions of this method are usedto detect changes in reservoir properties over time for reservoirmonitoring purposes.

The recordings of received waveforms are processed to generate an imageof the non-linear characteristics of the formation. The directivity ofthe beam and the time of flight may fix the locations where scatteredwaves are generated, distinguishing this device from normal sonicimaging techniques using conventional non-directional monopole anddipole sources.

Although the invention has been described in detail for the purpose ofillustration based on what is currently considered to be the mostpractical and preferred embodiments, it is to be understood that suchdetail is solely for that purpose and that the invention is not limitedto the disclosed embodiments, but, on the contrary, is intended to covermodifications and equivalent arrangements that are within the spirit andscope of the appended claims. As a further example, it is to beunderstood that the present invention contemplates that, to the extentpossible, one or more features of any embodiment can be combined withone or more features of any other embodiment.

1. An apparatus for estimating Vp/Vs ratio of the rock formations remotefrom a borehole using a conveyed logging tool, the apparatus comprising:a first source arranged in the borehole and configured to generateelastic energy at a first frequency; a second source arranged in theborehole and configured to generate elastic energy at a secondfrequency, wherein the energy at the first frequency and at the secondfrequency intersect at a location away from the borehole; a sensor arrayconfigured to receive a third elastic wave, the third elastic wave beingcreated by a non-linear mixing process from the elastic energy at thefirst frequency and the elastic energy at the second frequency in anon-linear mixing zone, the third elastic wave, having a frequency equalto a difference between the first and the second frequencies and adirection of propagation toward the borehole; and a processor arrangedto identify a location of the mixing zone based on the arrangement ofthe first and the second sources, the direction of the third wave andselection rules governing non-collinear mixing in acousticallynon-linear media, and to estimate Vp/Vs ratio based, in part, on thereceived third elastic wave and the arrangement of the first and secondsources.
 2. The apparatus according to claim 1, wherein the processor isfurther arranged to create the three-dimensional images based, in part,on properties of the received third wave and the arrangement of thefirst and second sources.
 3. The apparatus according to claim 1, furthercomprising: a device configured to transmit data up-hole through awireline cable for a wireline tool; and a subsequent processor arrangedin the borehole to control recordings of the third elastic wave.
 4. Theapparatus according to claim 1, wherein the first source and the secondsource are configured to generate elastic energy selected from the groupconsisting of: steerable beams, waves with limited directionality, andcombinations thereof.
 5. The apparatus according to claim 1, wherein thefirst source and the second source comprise an array of sources.
 6. Theapparatus according to claim 1, wherein the first source, the secondsource, and the sensor array are arranged either on a common tool bodyor on separate tool bodies.
 7. The apparatus according to claim 6,wherein the first source, the second source, and the sensor array arearranged on separate tool bodies, and the separate tool bodies can bemoved independently along a longitudinal axis of the borehole.
 8. Theapparatus according to claim 1, wherein the sensor array compriseseither one or more hydrophones mounted on a tool body, or one or morethree-component geophones, or accelerometers, clamped to the boreholewall, or both.
 9. The apparatus according to claim 1, wherein an azimuthand an inclination relative to a longitudinal axis of the borehole ofthe directions of propagation of the waves generated by one or both ofthe sources can be controlled.
 10. The apparatus according to claim 1,wherein the sensor array and the sources are arranged to be movedtogether or independently along the longitudinal axis of the borehole.11. The apparatus according to claim 1, wherein a plurality of radialscans is obtained by altering a spacing between the sources and thesensor array.
 12. The apparatus according to claim 1, wherein aplurality of radial scans is obtained by altering a spacing between thesources.
 13. The apparatus according to claim 1, wherein, at a givenborehole location, the second source is configured to be controlled at arange of frequencies f2 of the form f2=αf1, sweeping the values of α.14. The apparatus according to claim 1, wherein either or both of thefirst and the second waves are either chirped or coded or both chirpedand coded.
 15. The apparatus according to claim 14, wherein either thefirst or the second wave is modulated, and the modulation is selectedfrom the group consisting of: amplitude, phase, period and anycombination thereof.
 16. The apparatus according to claim 1, wherein ateach position related to a single azimuth, inclination and longitudinallocation, control of the sources is repeated, the second time with bothsignals at opposite polarity.
 17. The apparatus according to claim 1,wherein the processor is further configured and arranged to identify afrequency at which the received signal reaches a maximum amplitudestrength for each receiver in the sensor array and to measure in situVp/Vs ratio for the particular mixing region away from the borehole bydetermining the angle of intersection of the beams of the firstfrequency and the beams at the second frequency and a returning angle ofthe third elastic wave from the geometry of the first and the secondsources, the sensor array and selection rules governing non-linear andnon-collinear mixing properties.
 18. The apparatus according to claim 1,wherein the elastic energy at the first frequency is a compressionalelastic energy and the elastic energy at the second frequency is a shearelastic energy.